\frame{ \frametitle{Problem Definition}
  \begin{itemize}
    \item $X = \{x_i\}_{i=1}^{N_1} \in \mathbb{R}^N$
          is the data from the source domain; it has $M$ classes.
    \item $y_i \in \{1, 2, 3, \ldots, M\}$ is the class label for $x_i$.
    \item The data is mostly labeled. That is, $X = X_l \cup X_u$, where
          $X_l$ is the labelled data;
          $X_l = \{x_{li}\}_{i=1}^{N_{1i}}$ has labels
          $X_l = \{y_{li}\}_{i=1}^{N_{1i}}$ and the rest,
          $X_u = \{x_{ui}\}_{i=1}^{N_{ui}}$, has no labels,
          $N_1 = N_{u1} + N_{l1}$.
    \item Consider $\mathtt{X} = \{\mathtt{x}_i\}_{i=1}^{N_2} \in
          \mathbb{R}^N$, unlabelled data from the target domain.
  \end{itemize}
}

\frame{ \frametitle{Problem Definition: Source and Target}
  \includegraphics[width=\textwidth]{problem-definition}
}

\frame{ \frametitle{Problem Definition}
    \begin{itemize}
    \item Let $S_1$ and $S_2$ denote generative subspaces of
          dimension $N \times d$ obtained by
          principal component analysis
          (PCA) on $X$ and $\mathtt{X}$, respectively.
    \item The problem then is:
      \begin{enumerate}
        \item How to obtain the intermediate subspaces
              $S_t, t \in \mathbb{R}, 1 < t < 2$, and
        \item How to use $S_t$ on $X_l$ to obtain $\mathtt{X}$?
      \end{enumerate}
    \end{itemize}
}

\frame{ \frametitle{Problem Definition: Domain Adaptation}
  \includegraphics[width=\textwidth]{domain-adaptation}
}
